Another sequence that arises in this way is the regular paperfolding sequence \((p_n)_{n \in \mathbb {N}_+}\)  defined by \(p_{2n} = p_n\)  and \(p_{2n+1} = (-1)^n\)  (see for example [1]}). If we let \(P(x)= \sum _{n \ge 1} p_n x^n\) , then through manipulation of power series, for \(m\)  even one can obtain the congruence relation
\( B_m(x) \equiv (1-x)^m (1+2mP(x)) \pmod {*}{2^{\nu _2(m)+3}}. \) 
